file Optimal seatings changes 3R+F

11 Mar 2015 16:46 - 13 Mar 2017 10:06 #69811 by Ankha
Please disregard those results, for some of them are wrong due to a flaw in the validation.

From now on, I strongly recommand not to use the version 1.5e but version 1.5f :

Excel: www.vekn.net/images/stories/downloads/thearchon1.5f.xlsx
LibreOffice: www.vekn.net/images/stories/downloads/thearchon1.5f.ods


Ok, I've started toying with the 3R seatings.

Starting with 10 players, the current seating is :
12345|678910
101982|56437
471031|92586

with the following results:

RuleExpectedResult
N10
1. No pair of players repeat their predator-prey relationship. This is mandatory, by the VEKN rules.OK
2. No pair of players share a table through all two rounds, when possible. (N/A in some 2R event.)KO (player 1 shares a table with player 2 on round 2)
3. Available VPs are equitably distributed.OKOK
5. A player doesn't sit in the fifth seat more than once.OK
6. No pair of players repeat the same relative position[*], when possible.KO (players 8 and 10, table 1, round 2)
7. A player doesn't play in the same seat position, if possible.KO (player 7, table 1, position 2)
8. Starting transfers are equitably distributed. [NOAL]KO. Absolute deviation is: 1,04 => 1, 6 have 7 transfers | 2, 4, 5, 7, 9, 10 have 8 transfers | 3, 8 have 11 transfers

The first of the best results I have computed is:
12345|678910
862101|59473
103928|41756

with the following results:
RuleExpectedResult
N10
1. No pair of players repeat their predator-prey relationship. This is mandatory, by the VEKN rules.OK
2. No pair of players share a table through all two rounds, when possible. (N/A in some 2R event.)KO (player 1 shares a table with player 2 on round 2)
3. Available VPs are equitably distributed.OKOK
5. A player doesn't sit in the fifth seat more than once.OK
6. No pair of players repeat the same relative position[*], when possible.OK
7. A player doesn't play in the same seat position, if possible.OK
8. Starting transfers are equitably distributed. [NOAL]KO. Absolute deviation is: 0,72 => 1, 6 have 7 transfers | 2, 3, 5, 7, 9, 10 have 9 transfers | 4, 8 have 8 transfers


So compared to the current seating, rule 2 and 7 are no longer violated and the distribution of the transfers has a lesser deviation.
Plus, everyone has at least once 4 transfers.

Do you see anything unoptimal with the proposed new seating?

Prince of Paris, France
Ratings Coordinator, Rules Director
Last edit: 13 Mar 2017 10:06 by Ankha. Reason: Updated colors for white background
The following user(s) said Thank You: extrala

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12 Mar 2015 13:09 - 02 Mar 2017 09:41 #69831 by Ankha
Replied by Ankha on topic Re: Optimal seatings changes
8 players (3R): unchanged 7 1 8 2 | 3 5 4 6 / 4 7 6 1 | 8 3 2 5
Rule 2 KO (player 1 shares a table with player 2 on round 2): 12 (once), 12 (twice)
Rule 8 KO. Absolute deviation is: 1 => 1, 5 have 7 transfers | 2, 6 have 9 transfers | 3, 7 have 6 transfers | 4, 8 have 8 transfers

9 players (3R): unchanged 9 4 2 8 6 | 5 3 7 1 / 8 1 9 7 3 | 4 6 5 2
Rule 2 KO (player 1 shares a table with player 3 on round 2): 15 (once), 12 (twice), 3 (thrice)
Rule 3 KO. Absolute deviation is: 0,222 => 1, 2, 3, 4, 8, 9 have 14 VP | 5, 6, 7 have 13 VP
Rule 8 KO. Absolute deviation is: 0,666 => 1, 4, 6 have 7 transfers | 2, 3, 7 have 9 transfers | 5, 8, 9 have 8 transfers

10 players (3R): unchanged 10 1 9 8 2 | 5 6 4 3 7 / 4 7 10 3 1 | 9 2 5 8 6
Rule 2 KO. (player 1 shares a table with player 2 on round 2): 18 (once), 18 (twice), 2 (thrice))
Rule 6 and 7 KO.
Rule 8 KO. Absolute transfer deviation is: 1,04
The alternative seating (8 6 4 1 3 | 9 5 2 10 7 / 10 4 9 6 1 | 5 3 7 2 8 ) will not be kept because even though it doesn't violate rule 6 and 7 and has a better transfer deviation, it violates rule 2 with 3 pairs of players meeting thrice.

12 players (3R): 6 9 5 1 | 11 8 10 3 | 2 4 12 7 / 8 1 9 2 | 7 5 4 11 | 12 3 6 10
Rule 2 KO (player 2 shares a table with player 4 on round 2): 36 (once), 9 (twice)
(Current seating violates rule 2 (player 1 shares a table with player 2 on round 2): 30 (once), 12 (twice))
Rule 8 KO. Absolute deviation is: 1 => 1, 5, 9 have 7 transfers | 2, 6, 10 have 9 transfers | 3, 7, 11 have 6 transfers | 4, 8, 12 have 8 transfers

13 players (3R): 12 10 1 6 8 | 11 4 2 7 | 13 5 9 3 / 9 13 7 1 11 | 5 6 10 2 | 3 8 4 12
Rule 2 KO (player 2 shares a table with player 4 on round 2): 42 (once), 12 (twice)
(Current seating violates rule 2 (player 1 shares a table with player 3 on round 2): 34 (once), 16 (twice))
Rule 3 KO. Absolute deviation is: 0,071 => 1 have 15 VP | 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 have 13 VP
(Current seating has the same absolute vp deviation)
Rule 8 KO. Absolute deviation is: 0,804 => 1, 3, 9, 12 have 8 transfers | 2, 4, 7, 8 have 9 transfers | 5, 6, 11, 13 have 7 transfers | 10 have 6 transfers
(Current seating has the same absolute transfer deviation)

14 players (3R): 12 6 1 11 7 | 14 10 2 13 3 | 4 9 5 8 / 5 11 9 6 14 | 8 13 4 12 2 | 7 3 10 1
Rule 2 KO (player 2 shares a table with player 3 on round 2): 42 (once), 18 (twice)
(Current seating has the same encounter repartition)
Rule 3 KO. Absolute deviation is: 0,0612 => 1, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14 have 14 VP | 2, 6 have 15 VP
(Current seating has the same absolute deviation)
(Current seating violates rule 7: player 12, table 2, position 2)
Rule 8 KO. Absolute deviation is: 0,734 => 1, 4, 5, 8 have 8 transfers | 2, 3, 9, 10, 13, 14 have 9 transfers | 6, 7, 11, 12 have 7 transfers
(Current seating has an absolute deviation of 0,755)

15 players (3R): 5 11 6 1 12 | 13 4 7 2 8 | 9 3 15 10 14 / 14 1 4 11 7 | 12 15 2 6 9 | 10 8 5 13 3 (fixed in 1.5f)
Rule 2 KO (player 1 shares a table with player 5 on round 2): 54 (once), 18 (twice)
(Current seating has the same encounter repartition)
(Current seating also violate rule 6 and 7: player 8, table 1, position 3)
Rule 8 KO. Absolute deviation is: 0,72 => 1, 11, 12 have 7 transfers | 2, 3, 4, 7, 8, 9, 10, 14, 15 have 9 transfers | 5, 6, 13 have 8 transfers
(Current seating has an absolute deviation of 1,12)

16 players (3R): unchanged 8 1 14 11 | 12 5 2 15 | 16 9 6 3 | 4 13 10 7 / 15 7 1 9 | 10 16 8 2 | 3 11 13 5 | 6 4 12 14
Rule 8 KO.
(Current seating has an absolute transfer deviation of 1)

17 players (3R) (in progress) (fixed in 1.5f)

For 17 players, I had to "cheat" a little by entering manually some seatings (otherwise it would take 1 year to compute), so I don't know if there is a better solution. Anyway, this seating is slightly better.
What I did is that I chose 2 players that will never be seated on the only 5-players table (since only 15 players can be seated there through the 3 rounds). I chose players 12 and 17. I seated them in 4th, 3rd, 2nd position so they get in exchange the most transfers. The other players can only be seated once on the 5-players table, and I limited the number of players with 6 transfers to two.
Players 1 and 14 are 1st, 2nd and 3rd (6 transfers) but some players are necessarily disadvantaged.

EDIT:
The seating in the version 1.5d of the archon had two pairs of players meeting each other in a prey-predator then predator-prey way.
EDIT: the seating in version 1.5a had no violation of rule 1, therefore we use it until we found a better seating: 17 13 11 6 8 | 3 1 7 15 | 5 9 2 12 | 4 10 14 16 / 15 12 9 7 10 | 11 3 6 14 | 16 8 1 5 | 13 17 4 2

18 players (3R) 12 15 11 6 1 | 16 18 7 2 13 | 17 4 14 8 | 9 5 10 3 / 13 8 5 15 17 | 3 14 9 11 16 | 2 6 18 12 | 10 1 4 7
Rule 2 KO (player 3 shares a table with player 5 on round 2): 72 (once), 12 (twice)
(Current seating has a worse encounter repartition: 66 (once), 15 (twice))
Rule 3 KO. Absolute deviation is: 0,222 => 1, 2, 3, 5, 6, 7, 8, 9, 11, 13, 15, 16 have 14 VP | 4, 10, 12, 14, 17, 18 have 13 VP
(Current seating has the same absolute VP deviation.)
Rule 8 KO. Absolute deviation is: 0,666 => 1, 2, 6, 12, 15, 16 have 7 transfers | 3, 9, 10, 11, 13, 17 have 8 transfers | 4, 5, 7, 8, 14, 18 have 9 transfers
(Current seating has an absolute transfer deviation of 0,777)

19 players (3R): 12 4 11 6 16 | 17 14 7 18 1 | 2 19 9 13 8 | 5 10 15 3 / 13 3 10 17 11 | 18 5 19 12 6 | 15 8 1 16 7 | 14 9 4 2
KO (player 4 shares a table with player 5 on round 2): 84 (once), 12 (twice)
(Current seating has a the same encounter repartition)
Rule 3 KO. Absolute deviation is: 0,182 => 1, 2, 6, 7, 8, 11, 12 have 15 VP | 3, 4, 5, 9, 10, 13, 14, 15, 16, 17, 18, 19 have 14 VP
(Current seating has the same absolute vp deviation)
(Current seating violates rule 7.)
Rule 8 KO. Absolute deviation is: 0,747 => 1, 7, 11, 17, 19 have 7 transfers | 2, 4, 5, 12, 13, 14, 15, 16, 18 have 9 transfers | 3, 6, 8, 9, 10 have 8 transfers
(Current seating has an absolute transfer deviation of 0,831)

20 players (3R) (in progress): 3 1 14 10 17 | 8 6 19 15 2 | 13 11 4 20 7 | 18 16 9 5 12 / 15 19 7 1 13 | 20 4 12 6 18 | 5 9 17 11 3 | 10 14 2 16 8
Rule 8. KO. Absolute deviation is: 0,72 => 1, 6, 11, 16 have 7 transfers | 2, 4, 5, 7, 9, 10, 12, 14, 15, 17, 19, 20 have 9 transfers | 3, 8, 13, 18 have 8 transfers

21 players (3R): to revalidate fixed in 1.5f
The seating in 1.5a has a better score on rule 2. "No pair of players share a table through all two rounds, when possible. (N/A in some 2R event.)" It is used until we found something better

Prince of Paris, France
Ratings Coordinator, Rules Director
Last edit: 02 Mar 2017 09:41 by Ankha.

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26 Mar 2015 20:40 - 27 Mar 2015 06:25 #70091 by Ankha
Replied by Ankha on topic Re: Optimal seatings changes
Ok, we have a better seating for 15 players! Hooray!
If you see anything strange with this seating or have any comment, feel free to post!

In any case, it has a better transfer distribution, and more importantly, doesn't violate rules 6 and 7 anymore!

Prince of Paris, France
Ratings Coordinator, Rules Director
Last edit: 27 Mar 2015 06:25 by Ankha.

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27 Mar 2015 06:24 #70092 by Ankha
Replied by Ankha on topic Re: Optimal seatings changes
We also have a better seating for 14 players (better transfer distribution, and more importantly, it doesn't violate rule 7. "A player doesn't play in the same seat position, if possible." anymore!)

Prince of Paris, France
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27 Mar 2015 08:48 #70093 by Lönkka
Thank you SO much for putting time and energy for this!

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27 Mar 2015 20:35 #70101 by Hakuron

Thank you SO much for putting time and energy for this!

Seconded! B-)

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nc [dot] germany [at] magenta [dot] de

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